Rotate a point on a line at (−4, 6)

Question

(
−
4
,

6
)
180°
180
°
counterclockwise. What is the resulting point?(1 point)
Responses

(−6, 4)
(
−
6
,

4
)
left parenthesis negative 6 comma 4 right parenthesis

(6, −4)
(
6
,

−
4
)
left parenthesis 6 comma negative 4 right parenthesis

(4, −6)
(
4
,

−
6
)
left parenthesis 4 comma negative 6 right parenthesis

(−4, −6)
(
−
4
,

−
6
)
left parenthesis negative 4 com

Answer 1

To rotate a point 180° counterclockwise around a center point, we can use the following rule:

If we have a point \((x, y)\) and want to rotate it 180° around another point \((a, b)\), the resulting point will be \((2a - x, 2b - y)\).

In this case, our point is \((-4, 6)\) and we are rotating it around itself, which is also \((-4, 6)\).

Using the formula:

1. \(x' = 2(-4) - (-4) = -8 + 4 = -4\)
2. \(y' = 2(6) - 6 = 12 - 6 = 6\)

Thus, the point remains the same, \((-4, 6)\), after a 180° rotation around itself.

However, if you intended to rotate the point around the origin (0,0), then we would do the following:

For the point (-4, 6):

1. \(x' = -(-4) = 4\)
2. \(y' = -6\)

Thus, the resulting point after a 180° rotation around the origin is \((4, -6)\).

From your responses, the answer is: \((4, -6)\) (left parenthesis 4 comma negative 6 right parenthesis)